The Development of Neural Network Based System Identification ...

7.3 EXPERIMENTAL RESULTS 187
1
0.8
0.6
0.4
Imaginary Part
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1 −0.5 0 0.5 1
Real Part
Figure 7.1 The location of poles of the extracted linear models from the instantaneous linearisation
process. The poles were obtained at every simulation interval and are super-positions in the z-domain
plot.
7.3.1 Flight Controller Tuning
The proposed NNAPC design consists of three tuning parameters that need to be
properly tuned to achieve good controller performance. The tuning parameters that
influence the closed loop response of the system comprise the control horizon length N c ,
the control penalty factor r w and the prediction horizon length N p . The control horizon
value N c can be selected to be equal to or exceed the number of output lag (number
of past outputs) terms [Soeterboek, 1992]. Another way to determine the number of
control horizon N c steps is based on the number of unstable or poorly damped poles of
the system [Norgaard, 2000, Soeterboek, 1992]. Figure 7.1 shows the pole-zero map of
the coupled roll and pitch dynamic system of the unmanned helicopter system. The
result in this figure is obtained using the linear models extracted from the instantaneous
linearisation process at each sampling instant. In this study, the control horizon N c is
selected at 3 sample steps to exceed the number of poorly damped poles of the system.
Nevertheless, a higher number of control horizon N c can be selected for better controller
performance but at the expense of increased computation time.